SNA Interactive Plotting 1.2 - ALGUM RELACIONAMENTO (x2)
Leonardo Martins
17 de julho de 2016
- 1 1.2 - ALGUM RELACIONAMENTO (x2)
- 2 Removing CAPS AD
- 3 Density - The proportion of present edges from all possible edges in the network.
- 4 Vertex Connectivity - Group Cohesion
- 5 Centrality Measures
- 6 Centrality Degree Descriptive Statistics - non-normalized
- 7 Compute strength - weighted
- 8 Centrality Degree Normalized
- 8.1 Centrality Degree Normalized saving igraph object
- 8.2 Saving in Global Environment as an object
- 8.3 Centrality Degree Normalized Descriptive Statistics - in
- 8.4 Histogram x2_without_CAPS degree normalized - in
- 8.5 Centrality Degree Normalized Descriptive Statistics - out
- 8.6 Histogram x2_without_CAPS degree normalized - out
- 8.7 Centrality Degree Normalized Descriptive Statistics - all
- 8.8 Histogram x2_without_CAPS degree normalized - all
- 9 Centralization Degree
- 10 Degree distribution considering total equal one
- 11 Log-Log Degree Distribution - Scale Free Network - Does it fit to power law ?
- 12 Average Neighbor Degree versus Vertex Degree (log-log scale for 1.2 - ALGUM RELACIONAMENTO (x2))
- 13 Average Weighted Neighbor Degree versus vertex degree (log-log scale for weighted 1.2 - ALGUM RELACIONAMENTO (x2))
- 14 Degree Centralities Dinamic Table
- 14.1 Getting Degree Measures
- 14.2 Creating a dataframe of measures
- 14.3 General tabel - DT
- 14.4 Aggregating data from previous table - mean
- 14.5 Aggregating data from previous table - median
- 14.6 Merging mean and median
- 14.7 Plotting final table with round
- 14.8 Creating a dataframe of measures (Natureza Governamental)
- 14.9 General tabel - DT
- 14.10 Aggregating data from previous table - mean
- 14.11 Aggregating data from previous table - median
- 14.12 Merging mean and median
- 14.13 Plotting final table with round
- 14.14 Creating a dataframe of measures (Setores)
- 14.15 General tabel - DT
- 14.16 Aggregating data from previous table - mean
- 14.17 Aggregating data from previous table - median
- 14.18 Merging mean and median
- 14.19 Plotting final table with round
- 15 Network plotting based only on degree measures
- 16 Network plotting based only on degree measures
- 17 Network Plotting Centralization - Degree Measures - Using Spectral Color as Distance Measure Representation
- 18 Alternative vizualization using degree in order to genarete sub-graphs - Higher than median degree network
- 19 Alternative vizualization using degree in order to genarete sub-graphs - Lower than median degree network
- 20 Plotting using Average Neighbor Degree
- 21 Plotting using Average Neighbor Degree
- 22 Circle Degree Too intensive computation #code
- 23 Closeness - centrality based on distance to others in the graph
- 23.1 Closeness Non-normalized
- 23.2 Closeness Non-normalized - IN
- 23.3 Closeness Non-normalized - OUT
- 23.4 Closeness Non-normalized - ALL
- 23.5 Closeness Normalized
- 23.6 Network Plotting Based On Normalized Closeness - IN
- 23.7 Network Plotting Based On Normalized Closeness - OUT
- 23.8 Network Plotting Based On Normalized Closeness - ALL
- 23.9 Closeness Normalized
- 23.10 Centralization Closseness
- 23.11 Network Plotting Based On Centralization Closeness
- 24 Closeness Dinamic Table
- 24.1 Getting Closeness Measures
- 24.2 Creating a datagrame of measures
- 24.3 General tabel - DT
- 24.4 Aggregating data from previous table - mean
- 24.5 Aggregating data from previous table - median
- 24.6 Plotting final table with round for Closseness
- 24.7 Creating a datagrame of measures (Natureza Governamental)
- 24.8 General tabel - DT
- 24.9 Aggregating data from previous table - mean
- 24.10 Aggregating data from previous table - median
- 24.11 Plotting final table with round for Closseness
- 24.12 Creating a datagrame of measures (Setores)
- 24.13 General tabel - DT
- 24.14 Aggregating data from previous table - mean
- 24.15 Aggregating data from previous table - median
- 24.16 Plotting final table with round for Closseness
- 25 Betweenness - Number of shortest paths going through the actor σst(i)
- 26 Adding weight equal one for all analysis
- 27 Betweenness Vertex Centrality Dinamic Table
- 28 Betweenness Vertex Centrality Dinamic Table (Natureza Governamental)
- 29 Betweenness Vertex Centrality Dinamic Table (Setores)
- 29.1 General tabel for Betweenness
- 29.2 Aggregating data from previous table - mean
- 29.3 Aggregating data from previous table - median
- 29.4 Merging mean and median
- 29.5 Plotting final table with round
- 29.6 Plotting Betweenness Centrality - (Vertex)
- 29.7 Network Plotting Based On Centralization Betweenness
- 30 Reciprocity Default
- 31 Reciprocity Ratio
- 32 Dyad Census
- 33 Triad Census - Check this out in order to understand triad lables
- 34 Transitivity - clustering coefficient
- 35 Transitivity Local
- 36 Descriptive Statistics for Local Transitivity by Vertex
- 37 Barrat’s Weighted Transitivity by Edges (Barrat’s)
- 38 Descriptive Statistics for Barrat Weighted Transitivity by Vertex
- 39 Transitivity Measures Dinamic Table
- 40 Transitivity Measures Dinamic Table
- 41 Transitivity Measures Dinamic Table
- 42 Transitivity Measures Dinamic Table
- 43 Transitivity Measures Dinamic Table
- 44 Transitivity Measures Dinamic Table
- 45 Distances and paths
- 46 Length of all shortest paths in the graph:
- 47 In shortest paths
- 48 Out shortest paths
- 49 Reachbility Measures Dinamic Table
- 50 Reachbility Measures Dinamic Table
- 51 Reachbility Measures Dinamic Table
- 51.1 General tabel - DT
- 51.2 Aggregating data from previous table - mean
- 51.3 Aggregating data from previous table - median
- 51.4 Merging mean and median
- 51.5 Final table with round - Short Path
- 51.6 Histogram from shortest path length between each pair of vertices.
- 51.7 Simplify Graph - removing loops and duble edges
- 52 Find cliques (complete subgraphs of an undirected graph)
- 53 Saving objects with new variables and changes
SNA Descritive Analysis from “Projeto Redes de Atenção às pessoas que consomem álcool e outras Drogas em Juiz de Fora-MG Brazil” - SNArRDJF
Here you can find a basic script to analysis data from SNArRDJF - this script was elaborated considering its use for orther matrix adjacency data from SNArRDJF - Here we are going to analyse:
1 1.2 - ALGUM RELACIONAMENTO (x2)
########################## Basic Preparation ##### `#########################
1.1 Loading objects generated with 1.Principal.Rmd Script - Please run this script only after run 1.Principal.Rmd
1.2 Reload packages
suppressMessages(library(RColorBrewer))
suppressMessages(library(car))
suppressMessages(library(xtable))
suppressMessages(library(igraph))
suppressMessages(library(magrittr))
suppressMessages(library(keyplayer))
suppressMessages(library(dplyr))
suppressMessages(library(visNetwork))
suppressMessages(library(knitr))
suppressMessages(library(DT))1.3 Adding phantom tools
#In order to get dinamic javascript object install those ones. If you get problems installing go to Stackoverflow.com and type your error to discover what to do. In some cases the libraries need to be intalled in outside R libs.
#devtools::install_github("wch/webshot")
#webshot::install_phantomjs()1.4 Setting a random seed - this is a good strategy to keep the same graph pattern layout in a new report generation
set.seed(123)2 Removing CAPS AD
x2_without_CAPS<-delete_vertices(x2,V(x2)[V2_LABEL_ID=="q170_CAPS...CAPS.AD"])2.1 Vertices and Edges Number
#1. Vertices and Edges
x2_without_CAPS_vcount<-vcount(x2_without_CAPS)
x2_without_CAPS_ecount<-ecount(x2_without_CAPS)2.2 Vertice Number
Each vertice represents a service - named as an actor in our network
vcount(x2_without_CAPS)## [1] 1862.3 Edge Number
Each edge represents a connection between two services named as a tie
ecount(x2_without_CAPS)## [1] 13473 Density - The proportion of present edges from all possible edges in the network.
The density of a binary network is simply the proportion of all possible ties that are actually present.
For a valued network, density is defined as the sum of the ties divided by the number of possible ties (i.e. the ratio of all tie strength that is actually present to the number of possible ties).
The density of a network may give us insights into such phenomena as the speed at which information diffuses among the nodes, and the extent to which actors have high levels of social capital and/or social constraint.
3.1 Edge Density
The density of a graph is the ratio of the number of edges and the number of possible edges.
edge_density_x2_without_CAPS<-edge_density(x2_without_CAPS) #The proportion of present edges from all possible edges in the network.
edge_density_x2_without_CAPS## [1] 0.03914563.2 Edge connectivity - Adhesion
The edge connectivity of a graph or two vertices, this is recently also called group adhesion.
edge_connectivity(x2_without_CAPS, source =NULL, target =NULL, checks = T) #source and target can be replaced - their are here just as default## [1] 03.2.1 Adhesion example
In order to use this we need to call source and target using the number of each vertex instead of the name - type in R to get numbers
#Names and numbers
# list all if you have no idea about services id
# V(x2_without_CAPS)$name
# list all three first (you can use c(1:3))
V(x2_without_CAPS)$name[1] # just as an example## [1] "ASS_HOS_ Hospital de Pronto Socorro – HPS"V(x2_without_CAPS)$name[2] # just as an example## [1] "AMB_SAM_ Centro de Atenção à Saúde Mental (CASM)"V(x2_without_CAPS)$name[3] # just as an example## [1] "CRAS_AS_ CRAS Sudeste Costa Carvalho"# list by others id's
V(x2_without_CAPS)$name[6] # just as an example## [1] "ASS_HOS_ Serviço de Controle e Prevenção e Tratamento do Tabagismo (SECOPTT)"V(x2_without_CAPS)$name[150] # just as an example## [1] "UAP_RUR_ Jacutinga"V(x2_without_CAPS)$name[185] # just as an example## [1] "AJU_MUT_ Grupo N.A Rendição"3.3 Edge Connectivity - “CAPS_AD”==3 and “UAPS RURAL Buiéié”==150
Point connection calculates the number of nodes that would have to be removed in order for one actor to no longer be able to reach another. If there are many different pathways that connect two actors, they have high “connectivity” in the sense that there are multiple ways for a signal to reach from one to the other - lower number - worse resilience
edge_connectivity(x2_without_CAPS, source =150, target =3, checks = T) ## [1] 14 Vertex Connectivity - Group Cohesion
It is the minimum number of vertices needed to remove to make the graph not strongly connected. (If the graph is not strongly connected then this is zero.). The cohesion of a graph (as defined by White and Harary, see references), is the vertex connectivity of the graph. This is calculated by cohesion.
These three functions essentially calculate the same measure(s), more precisely vertex_connectivity is the most general, the other two are included only for the ease of using more descriptive function names.
vertex_connectivity(x2_without_CAPS, source = NULL, target = NULL, checks = TRUE)## [1] 04.1 Cohesion example
In order to use this we need to call source and target using the number of each vertex instead of the name - type in R to get numbers - see example above for more details
4.2 Vertex Connectivity - “CRE_SOC_ CREAS Norte”==6 and “AJU_MUT_ Grupo A.A. Liberdade” ==185
Minimum number of vertices needed to remove to make the vertex not connected by any vertex - it leads an error in case of using two connected vertex
vertex_connectivity(x2_without_CAPS, source =6, target =185, checks = T) ## [1] 15 Centrality Measures
• For undirected graphs:
– Actor centrality - involvement (connections) with other actors
• For directed graphs:
– Actor centrality - source of the ties (outgoing edges)
– Actor prestige - recipient of many ties (incoming edges)
In general - high centrality degree means direct contact with many other actors
5.1 Centrality Degree (number of ties/nearest neighbors).
5.2 Saving in igrpah object
V(x2_without_CAPS)$x2_indegree<-degree(x2_without_CAPS, mode = "in") # Actor prestige - recipient of many ties (incoming edges)
V(x2_without_CAPS)$x2_outdegree <- degree(x2_without_CAPS, mode = "out") # Actor centrality - source of the ties (outgoing edges)
V(x2_without_CAPS)$x2_totaldegree <- degree(x2_without_CAPS, mode = "total")5.3 Saving in Global Environment as an object
x2_without_CAPS_indegree<-degree(x2_without_CAPS, mode = "in")
x2_without_CAPS_outdegree<-degree(x2_without_CAPS, mode = "out")
x2_without_CAPS_totaldegree<-degree(x2_without_CAPS, mode = "total")6 Centrality Degree Descriptive Statistics - non-normalized
6.1 Centrality Degree Descriptive Statistics - In
##in
summary(x2_without_CAPS_indegree)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 3.000 4.500 7.242 8.000 69.000sd(x2_without_CAPS_indegree)## [1] 7.9512416.2 Histogram x2_without_CAPS degree - In
hist(degree(x2_without_CAPS, mode = "in", normalized = F), ylab="Frequency", xlab="Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of Indegree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
6.3 Centrality Degree Descriptive Statistics - Out
##out
summary(x2_without_CAPS_outdegree)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.000 3.000 7.242 8.000 88.000sd(x2_without_CAPS_outdegree)## [1] 11.832646.4 Histogram x2_without_CAPS degree - Out
hist(degree(x2_without_CAPS, mode = "out", normalized = F), ylab="Frequency", xlab="Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of Outdegree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
6.5 Centrality Degree Descriptive Statistics - All
##all
summary(x2_without_CAPS_totaldegree)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 4.00 8.00 14.48 16.00 157.00sd(x2_without_CAPS_totaldegree)## [1] 18.240216.6 Histogram x2_without_CAPS degree - All
hist(degree(x2_without_CAPS, mode = "all", normalized = F), ylab="Frequency", xlab="Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of All Degree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
7 Compute strength - weighted
A slightly more nuanced metric is “strength centrality”, which is defined as the sum of the weights of all the connections for a given node. This is also sometimes called “weighted degree centrality”
V(x2_without_CAPS)$x2_strength<- strength(x2_without_CAPS, weights=E(x2_without_CAPS)$weight)
x2_strength<- strength(x2_without_CAPS, weights=E(x2_without_CAPS)$weight)7.1 Strength Stats
summary(x2_strength)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 4.00 8.00 14.48 16.00 157.00sd(x2_strength)## [1] 18.240217.2 Histogram x2_without_CAPS degree - All
hist(strength(x2_without_CAPS, weights=E(x2_without_CAPS)$weight), ylab="Frequency", xlab="Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of Strength Degree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
8 Centrality Degree Normalized
8.1 Centrality Degree Normalized saving igraph object
V(x2_without_CAPS)$x2_indegree_n<-degree(x2_without_CAPS, mode = "in", normalized = T)
V(x2_without_CAPS)$x2_outdegree_n<- degree(x2_without_CAPS, mode = "out", normalized = T)
V(x2_without_CAPS)$x2_totaldegree_n<- degree(x2_without_CAPS, mode = "total", normalized = T)8.2 Saving in Global Environment as an object
x2_without_CAPS_indegree_n<-degree(x2_without_CAPS, mode = "in", normalized = T)
x2_without_CAPS_outdegree_n<-degree(x2_without_CAPS, mode = "out", normalized = T)
x2_without_CAPS_totaldegree_n<-degree(x2_without_CAPS, mode = "total", normalized = T)8.3 Centrality Degree Normalized Descriptive Statistics - in
summary(x2_without_CAPS_indegree_n)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00000 0.01622 0.02432 0.03915 0.04324 0.37300sd(x2_without_CAPS_indegree_n)## [1] 0.042979688.4 Histogram x2_without_CAPS degree normalized - in
hist(degree(x2_without_CAPS, mode = "in", normalized = T), ylab="Frequency", xlab="Normalized Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of Normalized Indegree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
8.5 Centrality Degree Normalized Descriptive Statistics - out
summary(x2_without_CAPS_outdegree_n)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000000 0.005405 0.016220 0.039150 0.043240 0.475700sd(x2_without_CAPS_outdegree_n)## [1] 0.063960238.6 Histogram x2_without_CAPS degree normalized - out
hist(degree(x2_without_CAPS, mode = "out", normalized = T), ylab="Frequency", xlab="Normalized Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of Normalized Outdegree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
8.7 Centrality Degree Normalized Descriptive Statistics - all
summary(x2_without_CAPS_totaldegree_n)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00000 0.02162 0.04324 0.07829 0.08649 0.84860sd(x2_without_CAPS_totaldegree_n)## [1] 0.098595718.8 Histogram x2_without_CAPS degree normalized - all
hist(degree(x2_without_CAPS, mode = "all", normalized = T), ylab="Frequency", xlab="Normalized Degree", breaks=vcount(x2_without_CAPS)/10, main="Histogram of Normalized All Degree Nodes - 1.2 - ALGUM RELACIONAMENTO (x2)")
9 Centralization Degree
V(x2_without_CAPS)$x2_centr_degree <- centralization.degree(x2_without_CAPS)$res
x2_centr_degree <- centralization.degree(x2_without_CAPS)9.1 Centralization
x2_centr_degree$centralization## [1] 0.38726089.2 Theoretical Max
x2_centr_degree$theoretical_max## [1] 6845010 Degree distribution considering total equal one
x2_without_CAPS_degree.distribution<-degree.distribution(x2_without_CAPS)10.1 Degree distribution Descriptive Stats
summary(x2_without_CAPS_degree.distribution)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000000 0.000000 0.000000 0.006329 0.005376 0.118300sd(x2_without_CAPS_degree.distribution)## [1] 0.0178624610.2 Histogram x2_without_CAPS distribution degree
hist(degree.distribution(x2_without_CAPS), breaks=vcount(x2_without_CAPS)/10, ylab="Frequency", xlab="Degree Distribuition", main="Histogram of Degree Distribuition - 1.2 - ALGUM RELACIONAMENTO (x2)")
10.3 Degree Probability Distribution
dd <- degree.distribution(x2_without_CAPS, cumulative=T, mode="all")10.4 Degree Probability Distribution - Plot Cumulative Frequency
plot(dd, pch=19, cex=1, col="orange", xlab="Degree", ylab="Cumulative Frequency", main= "Cumulative Frequency of 1.2 - ALGUM RELACIONAMENTO (x2) ")
11 Log-Log Degree Distribution - Scale Free Network - Does it fit to power law ?
dd.x2_without_CAPS <- degree.distribution(x2_without_CAPS)
d <- 1:max(degree(x2_without_CAPS))-1
ind <- (dd.x2_without_CAPS != 0)11.1 Plot Log-Log Degree Distribution
plot(d[ind],
dd.x2_without_CAPS[ind],
log="xy",
col="blue",
xlab=c("Log-Degree"),
ylab=c("Log-Intensity"),
main="Log-Log Degree Distribution For 1.2 - ALGUM RELACIONAMENTO (x2)"
)
12 Average Neighbor Degree versus Vertex Degree (log-log scale for 1.2 - ALGUM RELACIONAMENTO (x2))
The neighborhood of a given order y of a vertex v includes all vertices which are closer to v than the order. Ie. order y=0 is always v itself, order 1 is v plus its immediate neighbors, order 2 is order 1 plus the immediate neighbors of the vertices in order 1, etc.
12.1 Simplify graph first
x2_without_CAPS_simplified<-simplify(x2_without_CAPS)12.2 Average Neighbor Degree versus vertex degree (log-log scale for x2_without_CAPS)
x2_without_CAPS_a.nn.deg <- graph.knn(x2_without_CAPS_simplified, weights =E(x2_without_CAPS_simplified)$weight)$knn %>% round(1)12.3 Saving to igraph object
V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg <- graph.knn(x2_without_CAPS_simplified, weights=E(x2_without_CAPS_simplified)$weight)$knn12.4 Table Average Neighbor Degree
d<-cbind(V(x2_without_CAPS_simplified)$LABEL_COR,x2_without_CAPS_a.nn.deg)
datatable(d)12.5 Plotting Average Neighbor Degree versus vertex degree
plot(degree(x2_without_CAPS_simplified),
x2_without_CAPS_a.nn.deg,
log="xy",
col="goldenrod",
xlab=c("Log Vertex Degree"),
ylab=c("Log Average Neighbor Degree"),
main="Average Neighbor Degree vs Vertex Degree - Log-Log Scale for 1.2 - ALGUM RELACIONAMENTO (x2)"
)
13 Average Weighted Neighbor Degree versus vertex degree (log-log scale for weighted 1.2 - ALGUM RELACIONAMENTO (x2))
x2_without_CAPS_a.nn.deg_w <- graph.knn(x2_without_CAPS_simplified, weights=E(x2_without_CAPS_simplified)$weight)$knn %>% round(1)13.1 Saving to igraph object
V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w <-x2_without_CAPS_a.nn.deg <- graph.knn(x2_without_CAPS_simplified, weights=E(x2_without_CAPS_simplified)$weight)$knn13.2 Average Weighted Neighbor Descriptive
summary(x2_without_CAPS_a.nn.deg_w)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 4.00 29.20 41.20 46.28 57.20 128.50 1sd(x2_without_CAPS_a.nn.deg_w, na.rm = T)## [1] 25.0968313.3 Table Average Neighbor Degree Weighted
d<-cbind(V(x2_without_CAPS_simplified)$LABEL_COR,x2_without_CAPS_a.nn.deg_w)
datatable(d)13.4 Plotting Average Neighbor Degree versus vertex degree
plot(degree(x2_without_CAPS_simplified),
x2_without_CAPS_a.nn.deg,
log="xy",
col="goldenrod",
xlab=c("Log Vertex Degree"),
ylab=c("Log Average Neighbor Degree"),
main="Average Weighted Neighbor Degree vs Vertex Degree - Log-Log Scale For Weighted 1.2 - ALGUM RELACIONAMENTO (x2)"
)
14 Degree Centralities Dinamic Table
14.1 Getting Degree Measures
x2_without_CAPS_indegree<-degree(x2_without_CAPS, mode = "in")
x2_without_CAPS_outdegree<-degree(x2_without_CAPS, mode = "out")
x2_without_CAPS_totaldegree<-degree(x2_without_CAPS, mode = "total")
x2_strength<- strength(x2_without_CAPS, weights=E(x2_without_CAPS)$weight)
x2_without_CAPS_indegree_n<-degree(x2_without_CAPS, mode = "in", normalized = T) %>% round(3)
x2_without_CAPS_outdegree_n<-degree(x2_without_CAPS, mode = "out", normalized = T) %>% round(3)
x2_without_CAPS_totaldegree_n<-degree(x2_without_CAPS, mode = "total", normalized = T) %>% round(3)
x2_centr_degree <- centralization.degree(x2_without_CAPS)$res
x2_without_CAPS_a.nn.deg <- graph.knn(x2_without_CAPS_simplified)$knn %>% round(1)
x2_without_CAPS_a.nn.deg_w <- graph.knn(x2_without_CAPS_simplified, weights=E(x2_without_CAPS_simplified)$weight)$knn %>% round(1)14.2 Creating a dataframe of measures
x2_without_CAPS_df_degree <- data.frame(x2_without_CAPS_indegree,
x2_without_CAPS_outdegree,
x2_without_CAPS_totaldegree,
x2_without_CAPS_indegree_n,
x2_without_CAPS_outdegree_n,
x2_without_CAPS_totaldegree_n,
x2_strength,
x2_centr_degree,
x2_without_CAPS_a.nn.deg,
x2_without_CAPS_a.nn.deg_w) %>% round(3)
#Adding type
x2_without_CAPS_df_degree <-cbind(x2_without_CAPS_df_degree, V(x2_without_CAPS)$LABEL_COR)
#Adding names
names(x2_without_CAPS_df_degree) <- c("In Degree", "Out Degree", "Total Degree","In Degree Normalized", "Out Degree Normalized", "Total Degree Normalized", "Strength","Centralization Degree","Average Neighbor Degree","Average Weighted Neighbor Degree","Type")
#Ordering Variables
x2_without_CAPS_df_degree<-x2_without_CAPS_df_degree[c("Type","In Degree", "Out Degree", "Total Degree","In Degree Normalized", "Out Degree Normalized", "Total Degree Normalized", "Strength","Centralization Degree","Average Neighbor Degree","Average Weighted Neighbor Degree")]14.3 General tabel - DT
datatable(x2_without_CAPS_df_degree, filter = 'top')14.4 Aggregating data from previous table - mean
aggdata_mean <-aggregate(. ~ Type, x2_without_CAPS_df_degree, function(x) c(mean=mean(x)))
#Removing Type variable
names(aggdata_mean) <- c("Group", "In Degree(M)", "Out Degree(M)", "Total Degree(M)","In Degree Normalized(M)", "Out Degree Normalized(M)", "Total Degree Normalized(M)", "Strength(M)","Centralization Degree(M)","Average Neighbor Degree(M)","Average Weighted Neighbor Degree(M)")14.5 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_degree, function(x) c(median=median(x)))
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]
names(aggdata_median) <- c("Group", "In Degree(median)", "Out Degree(median)", "Total Degree(median)","In Degree Normalized(median)", "Out Degree Normalized(median)", "Total Degree Normalized(median)", "Strength(median)","Centralization Degree(median)","Average Neighbor Degree(median)","Average Weighted Neighbor Degree(median)")14.6 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(2) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","In Degree(M)","In Degree(median)", "Out Degree(M)", "Out Degree(median)","Total Degree(M)", "Total Degree(median)", "In Degree Normalized(M)", "In Degree Normalized(median)", "Out Degree Normalized(M)", "Out Degree Normalized(median)", "Total Degree Normalized(M)", "Total Degree Normalized(median)", "Strength(M)","Strength(median)", "Centralization Degree(M)","Centralization Degree(median)","Average Neighbor Degree(M)","Average Neighbor Degree(median)","Average Weighted Neighbor Degree(M)", "Average Weighted Neighbor Degree(median)")]14.7 Plotting final table with round
datatable(total_table, filter = 'top')14.8 Creating a dataframe of measures (Natureza Governamental)
x2_without_CAPS_df_degree <- data.frame(x2_without_CAPS_indegree,
x2_without_CAPS_outdegree,
x2_without_CAPS_totaldegree,
x2_without_CAPS_indegree_n,
x2_without_CAPS_outdegree_n,
x2_without_CAPS_totaldegree_n,
x2_strength,
x2_centr_degree,
x2_without_CAPS_a.nn.deg,
x2_without_CAPS_a.nn.deg_w) %>% round(3)
#Adding type
x2_without_CAPS_df_degree <-cbind(x2_without_CAPS_df_degree, V(x2_without_CAPS)$TIPO1)
#Adding names
names(x2_without_CAPS_df_degree) <- c("In Degree", "Out Degree", "Total Degree","In Degree Normalized", "Out Degree Normalized", "Total Degree Normalized", "Strength","Centralization Degree","Average Neighbor Degree","Average Weighted Neighbor Degree","Type")
#Ordering Variables
x2_without_CAPS_df_degree<-x2_without_CAPS_df_degree[c("Type","In Degree", "Out Degree", "Total Degree","In Degree Normalized", "Out Degree Normalized", "Total Degree Normalized", "Strength","Centralization Degree","Average Neighbor Degree","Average Weighted Neighbor Degree")]14.9 General tabel - DT
datatable(x2_without_CAPS_df_degree, filter = 'top')14.10 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_df_degree, by=list(x2_without_CAPS_df_degree$Type), FUN=mean, na.rm=TRUE)
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]
names(aggdata_mean) <- c("Group", "In Degree(M)", "Out Degree(M)", "Total Degree(M)","In Degree Normalized(M)", "Out Degree Normalized(M)", "Total Degree Normalized(M)", "Strength(M)","Centralization Degree(M)","Average Neighbor Degree(M)","Average Weighted Neighbor Degree(M)")14.11 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_degree, function(x) c(median=median(x)))
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]
names(aggdata_median) <- c("Group", "In Degree(median)", "Out Degree(median)", "Total Degree(median)","In Degree Normalized(median)", "Out Degree Normalized(median)", "Total Degree Normalized(median)", "Strength(median)","Centralization Degree(median)","Average Neighbor Degree(median)","Average Weighted Neighbor Degree(median)")14.12 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(2) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","In Degree(M)","In Degree(median)", "Out Degree(M)", "Out Degree(median)","Total Degree(M)", "Total Degree(median)", "In Degree Normalized(M)", "In Degree Normalized(median)", "Out Degree Normalized(M)", "Out Degree Normalized(median)", "Total Degree Normalized(M)", "Total Degree Normalized(median)", "Strength(M)","Strength(median)", "Centralization Degree(M)","Centralization Degree(median)","Average Neighbor Degree(M)","Average Neighbor Degree(median)","Average Weighted Neighbor Degree(M)", "Average Weighted Neighbor Degree(median)")]14.13 Plotting final table with round
datatable(total_table, filter = 'top')14.14 Creating a dataframe of measures (Setores)
x2_without_CAPS_df_degree <- data.frame(x2_without_CAPS_indegree,
x2_without_CAPS_outdegree,
x2_without_CAPS_totaldegree,
x2_without_CAPS_indegree_n,
x2_without_CAPS_outdegree_n,
x2_without_CAPS_totaldegree_n,
x2_strength,
x2_centr_degree,
x2_without_CAPS_a.nn.deg,
x2_without_CAPS_a.nn.deg_w) %>% round(3)
#Adding type
x2_without_CAPS_df_degree <-cbind(x2_without_CAPS_df_degree, V(x2_without_CAPS)$TIPO2)
#Adding names
names(x2_without_CAPS_df_degree) <- c("In Degree", "Out Degree", "Total Degree","In Degree Normalized", "Out Degree Normalized", "Total Degree Normalized", "Strength","Centralization Degree","Average Neighbor Degree","Average Weighted Neighbor Degree","Type")
#Ordering Variables
x2_without_CAPS_df_degree<-x2_without_CAPS_df_degree[c("Type","In Degree", "Out Degree", "Total Degree","In Degree Normalized", "Out Degree Normalized", "Total Degree Normalized", "Strength","Centralization Degree","Average Neighbor Degree","Average Weighted Neighbor Degree")]14.15 General tabel - DT
datatable(x2_without_CAPS_df_degree, filter = 'top')14.16 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_df_degree, by=list(x2_without_CAPS_df_degree$Type), FUN=mean, na.rm=TRUE)
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]
names(aggdata_mean) <- c("Group", "In Degree(M)", "Out Degree(M)", "Total Degree(M)","In Degree Normalized(M)", "Out Degree Normalized(M)", "Total Degree Normalized(M)", "Strength(M)","Centralization Degree(M)","Average Neighbor Degree(M)","Average Weighted Neighbor Degree(M)")14.17 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_degree, function(x) c(median=median(x)))
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]
names(aggdata_median) <- c("Group", "In Degree(median)", "Out Degree(median)", "Total Degree(median)","In Degree Normalized(median)", "Out Degree Normalized(median)", "Total Degree Normalized(median)", "Strength(median)","Centralization Degree(median)","Average Neighbor Degree(median)","Average Weighted Neighbor Degree(median)")14.18 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(2) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","In Degree(M)","In Degree(median)", "Out Degree(M)", "Out Degree(median)","Total Degree(M)", "Total Degree(median)", "In Degree Normalized(M)", "In Degree Normalized(median)", "Out Degree Normalized(M)", "Out Degree Normalized(median)", "Total Degree Normalized(M)", "Total Degree Normalized(median)", "Strength(M)","Strength(median)", "Centralization Degree(M)","Centralization Degree(median)","Average Neighbor Degree(M)","Average Neighbor Degree(median)","Average Weighted Neighbor Degree(M)", "Average Weighted Neighbor Degree(median)")]14.19 Plotting final table with round
datatable(total_table, filter = 'top')15 Network plotting based only on degree measures
#Set Seed
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$color[edge.start],
edge.arrow.size=(degree(x2_without_CAPS)+1)/(100*mean(degree(x2_without_CAPS))),
edge.width=E(x2_without_CAPS)$weight/(10*mean(E(x2_without_CAPS)$weight)),
edge.curved = TRUE,
vertex.size=log((degree(x2_without_CAPS)+2))*(0.5*mean(degree(x2_without_CAPS))),
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=log(degree(x2_without_CAPS)+2)/mean(degree(x2_without_CAPS)),
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2]))
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$LABEL_COR
b<-V(x2_without_CAPS)$color
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2], y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .5)
#Adding Title
title("Network Vertex Degree Sized - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ", cex = .5)
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Median In Degree: %.2f\n Median Out Degree: %.2f",
median(degree(x2_without_CAPS, mode="in")),
median(degree(x2_without_CAPS, mode="out"))
))
16 Network plotting based only on degree measures
#Set Seed
set.seed(123)
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-V(x2_without_CAPS)$x2_totaldegree %>% round(1)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<- x2_vertex_color_degree[as.numeric(cut(degree(x2_without_CAPS),breaks =length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
#edge.color=V(x2_without_CAPS)$color[edge.start],
edge.arrow.size=(degree(x2_without_CAPS)+1)/3000,
edge.width=E(x2_without_CAPS)$weight/10,
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=log((degree(x2_without_CAPS)+2))*10,
vertex.size=20,
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=log((degree(x2_without_CAPS)+2))/10,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2], y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Vertex Degree Sized and Red to Blue - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Median In Degree: %.2f\nMedian Out Degree: %.2f",
median(degree(x2_without_CAPS, mode="in")),
median(degree(x2_without_CAPS, mode="out"))
))
17 Network Plotting Centralization - Degree Measures - Using Spectral Color as Distance Measure Representation
#Set Seed
set.seed(123)
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-V(x2_without_CAPS)$x2_centr_degree
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "Spectral"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<- x2_vertex_color_degree[as.numeric(cut(V(x2_without_CAPS)$x2_color_degree,breaks =length(unique(V(x2_without_CAPS)$x2_color_degree))))]
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=(degree(x2_without_CAPS)+1)/10000,
edge.width=E(x2_without_CAPS)$weight/10,
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=log((V(x2_without_CAPS)$x2_centr_degree+2))*10,
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=log((degree(x2_without_CAPS)+2))/10,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2]))
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2], y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Vertex Centralization Degree Sized Spectral Colored - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Median In Degree: %.2f\nMedian Out Degree: %.2f",
median(degree(x2_without_CAPS, mode="in")),
median(degree(x2_without_CAPS, mode="out"))
))
18 Alternative vizualization using degree in order to genarete sub-graphs - Higher than median degree network
#Set Seed
set.seed(123)
# Network elements with lower than meadian degree
higherthanmedian.network_x2_without_CAPS<-V(x2_without_CAPS)[degree(x2_without_CAPS)<median(degree(x2_without_CAPS))]
#Deleting vertices based in intersection betewenn x2_without_CAPS
high_x2_without_CAPS<-delete.vertices(x2_without_CAPS, higherthanmedian.network_x2_without_CAPS)
#Plotting based only on degree measures
edge.start <- ends(high_x2_without_CAPS, es=E(high_x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(high_x2_without_CAPS))
maxC <- rep(Inf, vcount(high_x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(high_x2_without_CAPS, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(high_x2_without_CAPS)$weight)
#PLotting
plot(high_x2_without_CAPS,
layout=co,
edge.color=V(high_x2_without_CAPS)$color[edge.start],
edge.arrow.size=(degree(high_x2_without_CAPS)+1)/1000,
edge.width=E(high_x2_without_CAPS)$weight/10,
edge.curved = TRUE,
vertex.size=log((V(high_x2_without_CAPS)$x2_centr_degree+2))*10,
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(high_x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=log((degree(high_x2_without_CAPS)+2))/10,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2]))
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(high_x2_without_CAPS)$LABEL_COR
b<-V(high_x2_without_CAPS)$color
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2], y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=3,
bty="n",
ncol=1,
lty=1,
cex = .5)
#Adding Title
title("Network Higher Than Median Degree - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Mean In Degree: %.2f\n Mean Out Degree: %.2f",
mean(degree(high_x2_without_CAPS, mode="in")),
mean(degree(high_x2_without_CAPS, mode="out"))
)
)
19 Alternative vizualization using degree in order to genarete sub-graphs - Lower than median degree network
#Set Seed
set.seed(123)
# Network elements with lower than meadian degree
lowerthanmedian.network_x2_without_CAPS<-V(x2_without_CAPS)[degree(x2_without_CAPS)>median(degree(x2_without_CAPS))]
#Deleting vertices based in intersection betewenn x2_without_CAPS
small_x2_without_CAPS<-delete.vertices(x2_without_CAPS, lowerthanmedian.network_x2_without_CAPS)
#Plotting based only on degree measures
edge.start <- ends(small_x2_without_CAPS, es=E(small_x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(small_x2_without_CAPS))
maxC <- rep(Inf, vcount(small_x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(small_x2_without_CAPS, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(small_x2_without_CAPS)$weight)
#PLotting
plot(small_x2_without_CAPS,
layout=co,
edge.color=V(small_x2_without_CAPS)$color[edge.start],
edge.arrow.size=(degree(small_x2_without_CAPS)+1)/1000,
edge.width=E(small_x2_without_CAPS)$weight/10,
edge.curved = TRUE,
vertex.size=log((V(small_x2_without_CAPS)$x2_centr_degree+2))*20,
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(small_x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=log((degree(small_x2_without_CAPS)+2))/3,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2]))
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(small_x2_without_CAPS)$LABEL_COR
b<-V(small_x2_without_CAPS)$color
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2], y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=4,
bty="n",
ncol=1,
lty=1,
cex = .5)
#Adding Title
title("Network Smaller Than Median Degree - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Mean In Degree: %.2f\nMean Out Degree: %.2f",
mean(degree(small_x2_without_CAPS, mode="in")),
mean(degree(small_x2_without_CAPS, mode="out"))
)
)
20 Plotting using Average Neighbor Degree
#Set Seed
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS_simplified, es=E(x2_without_CAPS_simplified), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS_simplified))
maxC <- rep(Inf, vcount(x2_without_CAPS_simplified))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS_simplified, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS_simplified)$weight)
#Plotting based only on degree measures #x2_without_CAPS_simplified_a.nn.deg
V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg<-as.numeric(graph.knn(x2_without_CAPS_simplified)$knn)
V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg[V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg=="NaN"]<-0
#PLotting
plot(x2_without_CAPS_simplified,
layout=co,
edge.color=V(x2_without_CAPS_simplified)$color[edge.start],
edge.arrow.size=sqrt((V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg)^2+1)/1000,
edge.width=E(x2_without_CAPS_simplified)$weight/80,
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS_simplified)$color,
vertex.size=(sqrt((V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg)^2))/1,
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS_simplified,"LABEL_COR"),
vertex.label.cex=(sqrt((V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg)^2)+1)/250,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2]))
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS_simplified)$LABEL_COR
b<-V(x2_without_CAPS_simplified)$color
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
inset=2,
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=3,
lwd=2,
x.intersp=2,
y.intersp=4,
cex = .3)
#Adding Title
title("Network Average Neighbor Degree Sized - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Median Average Neighbor Degree: %.2f",
median((x2_without_CAPS_a.nn.deg+1))
))
21 Plotting using Average Neighbor Degree
#Set Seed
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS_simplified, es=E(x2_without_CAPS_simplified), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS_simplified))
maxC <- rep(Inf, vcount(x2_without_CAPS_simplified))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS_simplified, niter=10000, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS_simplified)$weight)
#Plotting based only on degree measures #x2_without_CAPS_a.nn.deg
V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w<-as.numeric(graph.knn(x2_without_CAPS_simplified, weights = E(x2_without_CAPS_simplified)$weight)$knn)
V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w[V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w=="NaN"]<-0
#PLotting
plot(x2_without_CAPS_simplified,
layout=co,
edge.color=V(x2_without_CAPS_simplified)$color[edge.start],
edge.arrow.size=sqrt((V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w)^2+1)/1000,
edge.width=E(x2_without_CAPS_simplified)$weight/100,
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS_simplified)$color,
vertex.size=(sqrt((V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w)^2))/5,
vertex.frame.color="#ffffff",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS_simplified,"LABEL_COR"),
vertex.label.cex=(sqrt((V(x2_without_CAPS_simplified)$x2_without_CAPS_a.nn.deg_w)^2)+1)/500,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2]))
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS_simplified)$LABEL_COR
b<-V(x2_without_CAPS_simplified)$color
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2], y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=4,
bty="n",
ncol=1,
lty=1,
cex = .5)
#Adding Title
title("Network Average Weighted Neighbor Degree Sized - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(x=range(co[,1])[1], y=range(co[,2])[1], labels =
sprintf("Median Average Weighted Neighbor Degree: %.2f",
median((x2_without_CAPS_a.nn.deg_w+1))
))
22 Circle Degree Too intensive computation #code
#Circle Degree ***Too intense computation***
#A_x2_without_CAPS <- get.adjacency(x2_without_CAPS, sparse=FALSE)
#detach("package:igraph", unload=TRUE)
#library(network)
#g <- network::as.network.matrix(A_x2_without_CAPS)
#library(sna)
#gplot.target(g, degree(g), main="Circle Degree")
#library(igraph)23 Closeness - centrality based on distance to others in the graph
How close an actor to all the other actors in network?
High closeness centrality - short communication path to others, minimal number of steps to reach others.
Answers the “Kevin Bacon” question:
How many steps are required to access every other vertex from a given vertex?
One practical implication of this metric: it helps you gauge how information might spread within your network, and who might be the best people to leverage if you need to make sure information gets around. Link here: http://www.tc.umn.edu/~alink/R-social-network-analysis.html
Closeness centrality can be defined as a measure of how far other nodes are from the node in question. Nodes with high closeness centrality are likely to be relatively efficient in receiving or transmitting information to/from distant parts of the social network.
Scores may be interpreted as arising from a reciprocal process in which the centrality of each actor is proportional to the sum of the centralities of those actors to whom he or she is connected.
In general, vertices with high eigenvector centralities are those which are connected to many other vertices which are, in turn, connected to many others (and so on). (The perceptive may realize that this implies that the largest values will be obtained by individuals in large cliques (or high-density substructures)
23.1 Closeness Non-normalized
23.1.1 Saving to Igraph object
V(x2_without_CAPS)$x2_incloseness <- closeness(x2_without_CAPS, mode = "in", weights = E(x2_without_CAPS)$x2) %>% round(6)
V(x2_without_CAPS)$x2_outcloseness <- closeness(x2_without_CAPS, mode = "out", weights = E(x2_without_CAPS)$x2) %>% round(6)
V(x2_without_CAPS)$x2_totalcloseness <- closeness(x2_without_CAPS, mode = "total", weights = E(x2_without_CAPS)$x2) %>% round(4)23.1.2 Saving to Environment
x2_without_CAPS_incloseness<- closeness(x2_without_CAPS, mode = "in", weights = E(x2_without_CAPS)$x2) %>% round(6)
x2_without_CAPS_outcloseness<- closeness(x2_without_CAPS, mode = "out", weights = E(x2_without_CAPS)$x2) %>% round(6)
x2_without_CAPS_totalcloseness<- closeness(x2_without_CAPS, mode = "total", weights = E(x2_without_CAPS)$x2) %>% round(6)23.2 Closeness Non-normalized - IN
summary(x2_without_CAPS_incloseness)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.900e-05 1.000e-04 1.000e-04 9.939e-05 1.000e-04 1.050e-04sd(x2_without_CAPS_incloseness)## [1] 7.438523e-0623.2.1 Network Plotting Based On Non-normalized Closeness - IN
V(x2_without_CAPS)$x2_incloseness<-closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in")
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_incloseness,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in"),
edge.width=E(x2_without_CAPS)$weight/mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in")*10^5,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=(closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in")+10^-5)*2000,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Closeness Degree Sized and Colored In - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median In Closennes:%.4f\nSD In Closennes: %.5f",
median(closeness(x2_without_CAPS, mode="in", weights = E(x2_without_CAPS)$x2)),
sd(closeness(x2_without_CAPS, mode="in", weights = E(x2_without_CAPS)$x2))
)
)
23.3 Closeness Non-normalized - OUT
summary(x2_without_CAPS_outcloseness)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000290 0.0000290 0.0011000 0.0008432 0.0012130 0.0014580sd(x2_without_CAPS_outcloseness)## [1] 0.000517582923.3.1 Network Plotting Based On Non-normalized Closeness - OUT
V(x2_without_CAPS)$x2_outcloseness<-closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out")
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_outcloseness,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out"),
edge.width=E(x2_without_CAPS)$weight/2*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out")*10^4,
vertex.frame.color="white",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out")*200,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Closeness Degree Sized and Colored OUT - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median OUT Closennes:%.4f\nSD OUT Closennes: %.5f",
median(closeness(x2_without_CAPS, mode="out", weights = E(x2_without_CAPS)$x2)),
sd(closeness(x2_without_CAPS, mode="out", weights = E(x2_without_CAPS)$x2))
)
)
23.4 Closeness Non-normalized - ALL
summary(x2_without_CAPS_totalcloseness)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000029 0.001529 0.001642 0.001615 0.001710 0.002227sd(x2_without_CAPS_totalcloseness)## [1] 0.000193335323.4.1 Network Plotting Based On Non-normalized Closeness - ALL
V(x2_without_CAPS)$x2_allcloseness<-closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all")
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_allcloseness,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all"),
edge.width=E(x2_without_CAPS)$weight/2*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all")*10^4,
vertex.frame.color="white",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=(closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all")+0.00001)*200,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Closeness Degree Sized and Colored all - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median all Closennes:%.4f\nSD all Closennes: %.5f",
median(closeness(x2_without_CAPS, mode="all", weights = E(x2_without_CAPS)$x2)),
sd(closeness(x2_without_CAPS, mode="all", weights = E(x2_without_CAPS)$x2))
)
)
23.5 Closeness Normalized
23.5.1 Saving to Igraph object
V(x2_without_CAPS)$x2_incloseness_n <- closeness(x2_without_CAPS, mode = "in",, weights = E(x2_without_CAPS)$x2, normalized = T) %>% round(10)
V(x2_without_CAPS)$x2_outcloseness_n <- closeness(x2_without_CAPS, mode = "out", normalized = T, weights = E(x2_without_CAPS)$x2) %>% round(6)
V(x2_without_CAPS)$x2_totalcloseness_n <- closeness(x2_without_CAPS, mode = "total", normalized = T, weights = E(x2_without_CAPS)$x2) %>% round(6)23.5.2 Saving to Environment
x2_without_CAPS_incloseness_n<- closeness(x2_without_CAPS, mode = "in", normalized = T, weights = E(x2_without_CAPS)$x2) %>% round(6)
x2_without_CAPS_outcloseness_n<- closeness(x2_without_CAPS, mode = "out", normalized = T, weights = E(x2_without_CAPS)$x2) %>% round(6)
x2_without_CAPS_totalcloseness_n<- closeness(x2_without_CAPS, mode = "total", normalized = T, weights = E(x2_without_CAPS)$x2) %>% round(6)23.5.3 Closeness Normalized - IN
summary(x2_without_CAPS_incloseness_n)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.005376 0.018460 0.018530 0.018400 0.018590 0.019340sd(x2_without_CAPS_incloseness_n)## [1] 0.00137489723.6 Network Plotting Based On Normalized Closeness - IN
V(x2_without_CAPS)$x2_incloseness_n<-closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in", normalized = T)
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_incloseness_n,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in",normalized = T),
edge.width=E(x2_without_CAPS)$weight/1000*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=(closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in",normalized = T))*10000,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="in",normalized = T)*10,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Closeness Degree Sized Normalized In - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median In Closennes:%.4f\nSD In Closennes: %.5f",
median(closeness(x2_without_CAPS, mode="in", weights = E(x2_without_CAPS)$x2, normalized = T)),
sd(closeness(x2_without_CAPS, mode="in", weights = E(x2_without_CAPS)$x2, normalized = T))
)
)
###Closeness Normalized - OUT
summary(x2_without_CAPS_outcloseness_n)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.005376 0.005383 0.203600 0.156000 0.224300 0.269700sd(x2_without_CAPS_outcloseness_n)## [1] 0.0957459223.7 Network Plotting Based On Normalized Closeness - OUT
V(x2_without_CAPS)$x2_outcloseness_n<-closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out", normalized = T)
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_outcloseness_n,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out",normalized = T),
edge.width=E(x2_without_CAPS)$weight/10*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=(closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out",normalized = T))*100,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out",normalized = T)*1.5,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Closeness Degree Sized Normalized OUT - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median OUT Closennes:%.4f\nSD OUT Closennes: %.5f",
median(closeness(x2_without_CAPS, mode="out", weights = E(x2_without_CAPS)$x2, normalized = T)),
sd(closeness(x2_without_CAPS, mode="out", weights = E(x2_without_CAPS)$x2, normalized = T))
)
)
23.7.1 Closeness Normalized - ALL
summary(x2_without_CAPS_totalcloseness_n)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.005376 0.282900 0.303800 0.298900 0.316500 0.412000sd(x2_without_CAPS_totalcloseness_n)## [1] 0.0357701923.8 Network Plotting Based On Normalized Closeness - ALL
V(x2_without_CAPS)$x2_allcloseness_n<-closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all", normalized = T)
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_allcloseness_n,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "RdBu"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all",normalized = T),
edge.width=E(x2_without_CAPS)$weight/10*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=(closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all",normalized = T))*100,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="all",normalized = T)*1.5,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Closeness Degree Sized Normalized ALL - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median ALL Closennes:%.4f\nSD ALL Closennes: %.5f",
median(closeness(x2_without_CAPS, mode="all", weights = E(x2_without_CAPS)$x2, normalized = T)),
sd(closeness(x2_without_CAPS, mode="all", weights = E(x2_without_CAPS)$x2, normalized = T))
)
)
23.9 Closeness Normalized
23.9.1 Saving to Igraph object
V(x2_without_CAPS)$x2_incloseness_n <- closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode = "in", normalized = T) %>% round(6)
V(x2_without_CAPS)$x2_outcloseness_n <- closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode = "out", normalized = T) %>% round(6)
V(x2_without_CAPS)$x2_totalcloseness_n <- closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode = "total", normalized = T) %>% round(6)23.10 Centralization Closseness
V(x2_without_CAPS)$x2_centr_closeness<- centralization.closeness(x2_without_CAPS)$res
x2_centr_closeness<- centralization.closeness(x2_without_CAPS)$res
x2_without_CAPS_centr_closeness_all<- centralization.closeness(x2_without_CAPS)23.10.1 Centralization
x2_without_CAPS_centr_closeness_all$centralization## [1] 0.114922523.10.2 Theoretical Max
x2_without_CAPS_centr_closeness_all$theoretical_max## [1] 184.005423.11 Network Plotting Based On Centralization Closeness
V(x2_without_CAPS)$x2_centr_closeness<- centralization.closeness(x2_without_CAPS)$res
#Get Variable
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_centr_closeness,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "Spectral"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=centralization.closeness(x2_without_CAPS)$res,
edge.width=E(x2_without_CAPS)$weight/10*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=centralization.closeness(x2_without_CAPS)$res*100,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=centralization.closeness(x2_without_CAPS)$res,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Centralization Closeness - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf(
"Median Centralization Closeness:%.4f\nSD Centralization Closeness: %.5f",
median(centralization.closeness(x2_without_CAPS)$res),
sd(centralization.closeness(x2_without_CAPS)$res)
)
)
24 Closeness Dinamic Table
24.1 Getting Closeness Measures
x2_without_CAPS_incloseness<- closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode = "in") %>% round(6)
x2_without_CAPS_outcloseness<- closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode = "out") %>% round(6)
x2_without_CAPS_totalcloseness<- closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode = "total") %>% round(6)
x2_without_CAPS_incloseness_n<- closeness(x2_without_CAPS,weights = E(x2_without_CAPS)$x2, mode = "in", normalized = T) %>% round(6)
x2_without_CAPS_outcloseness_n<- closeness(x2_without_CAPS,weights = E(x2_without_CAPS)$x2, mode = "out", normalized = T) %>% round(6)
x2_without_CAPS_totalcloseness_n<- closeness(x2_without_CAPS,weights = E(x2_without_CAPS)$x2, mode = "total", normalized = T) %>% round(6)
x2_centr_closeness <- centralization.closeness(x2_without_CAPS)$res %>% round(6)24.2 Creating a datagrame of measures
x2_without_CAPS_df_closseness <- data.frame(
x2_without_CAPS_incloseness,
x2_without_CAPS_outcloseness,
x2_without_CAPS_totalcloseness,
x2_without_CAPS_incloseness_n,
x2_without_CAPS_outcloseness_n,
x2_without_CAPS_totalcloseness_n,
x2_centr_closeness) %>% round(6)
#Adding type
x2_without_CAPS_df_closseness <-cbind(x2_without_CAPS_df_closseness, V(x2_without_CAPS)$LABEL_COR)
#Adding names
names(x2_without_CAPS_df_closseness) <- c("In Closeness", "Out Closeness", "Total Closeness","In Closeness Normalized", "Out Closeness Normalized", "Total Closeness Normalized","Centralization Closeness","Type")
#Ordering Variables
x2_without_CAPS_df_closseness<-x2_without_CAPS_df_closseness[c("Type","In Closeness", "Out Closeness", "Total Closeness","In Closeness Normalized", "Out Closeness Normalized","Total Closeness Normalized", "Centralization Closeness")]24.3 General tabel - DT
datatable(x2_without_CAPS_df_closseness, filter = 'top')24.4 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_df_closseness, by=list(x2_without_CAPS_df_closseness$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","In Closeness(M)", "Out Closeness(M)", "Total Closeness(M)","In Closeness Normalized(M)", "Out Closeness Normalized(M)", "Total Closeness Normalized(M)","Centralization Closeness(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]24.5 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_closseness, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","In Closeness(median)", "Out Closeness(median)", "Total Closeness(median)","In Closeness Normalized(median)", "Out Closeness Normalized(median)", "Total Closeness Normalized(median)", "Centralization Closeness(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]
#Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(6) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","In Closeness(M)", "In Closeness(median)", "Out Closeness(M)", "Out Closeness(median)", "Total Closeness(M)","Total Closeness(median)","In Closeness Normalized(M)", "In Closeness Normalized(median)", "Out Closeness Normalized(M)", "Out Closeness Normalized(median)", "Total Closeness Normalized(M)","Total Closeness Normalized(median)", "Centralization Closeness(M)","Centralization Closeness(median)")]24.6 Plotting final table with round for Closseness
datatable(total_table, filter = 'top')24.7 Creating a datagrame of measures (Natureza Governamental)
x2_without_CAPS_df_closseness <- data.frame(
x2_without_CAPS_incloseness,
x2_without_CAPS_outcloseness,
x2_without_CAPS_totalcloseness,
x2_without_CAPS_incloseness_n,
x2_without_CAPS_outcloseness_n,
x2_without_CAPS_totalcloseness_n,
x2_centr_closeness) %>% round(6)
#Adding type
x2_without_CAPS_df_closseness <-cbind(x2_without_CAPS_df_closseness, V(x2_without_CAPS)$TIPO1)
#Adding names
names(x2_without_CAPS_df_closseness) <- c("In Closeness", "Out Closeness", "Total Closeness","In Closeness Normalized", "Out Closeness Normalized", "Total Closeness Normalized","Centralization Closeness","Type")
#Ordering Variables
x2_without_CAPS_df_closseness<-x2_without_CAPS_df_closseness[c("Type","In Closeness", "Out Closeness", "Total Closeness","In Closeness Normalized", "Out Closeness Normalized","Total Closeness Normalized", "Centralization Closeness")]24.8 General tabel - DT
datatable(x2_without_CAPS_df_closseness, filter = 'top')24.9 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_df_closseness, by=list(x2_without_CAPS_df_closseness$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","In Closeness(M)", "Out Closeness(M)", "Total Closeness(M)","In Closeness Normalized(M)", "Out Closeness Normalized(M)", "Total Closeness Normalized(M)","Centralization Closeness(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]24.10 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_closseness, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","In Closeness(median)", "Out Closeness(median)", "Total Closeness(median)","In Closeness Normalized(median)", "Out Closeness Normalized(median)", "Total Closeness Normalized(median)", "Centralization Closeness(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]
#Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(6) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","In Closeness(M)", "In Closeness(median)", "Out Closeness(M)", "Out Closeness(median)", "Total Closeness(M)","Total Closeness(median)","In Closeness Normalized(M)", "In Closeness Normalized(median)", "Out Closeness Normalized(M)", "Out Closeness Normalized(median)", "Total Closeness Normalized(M)","Total Closeness Normalized(median)", "Centralization Closeness(M)","Centralization Closeness(median)")]24.11 Plotting final table with round for Closseness
datatable(total_table, filter = 'top')24.12 Creating a datagrame of measures (Setores)
x2_without_CAPS_df_closseness <- data.frame(
x2_without_CAPS_incloseness,
x2_without_CAPS_outcloseness,
x2_without_CAPS_totalcloseness,
x2_without_CAPS_incloseness_n,
x2_without_CAPS_outcloseness_n,
x2_without_CAPS_totalcloseness_n,
x2_centr_closeness) %>% round(6)
#Adding type
x2_without_CAPS_df_closseness <-cbind(x2_without_CAPS_df_closseness, V(x2_without_CAPS)$TIPO2)
#Adding names
names(x2_without_CAPS_df_closseness) <- c("In Closeness", "Out Closeness", "Total Closeness","In Closeness Normalized", "Out Closeness Normalized", "Total Closeness Normalized","Centralization Closeness","Type")
#Ordering Variables
x2_without_CAPS_df_closseness<-x2_without_CAPS_df_closseness[c("Type","In Closeness", "Out Closeness", "Total Closeness","In Closeness Normalized", "Out Closeness Normalized","Total Closeness Normalized", "Centralization Closeness")]24.13 General tabel - DT
datatable(x2_without_CAPS_df_closseness, filter = 'top')24.14 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_df_closseness, by=list(x2_without_CAPS_df_closseness$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","In Closeness(M)", "Out Closeness(M)", "Total Closeness(M)","In Closeness Normalized(M)", "Out Closeness Normalized(M)", "Total Closeness Normalized(M)","Centralization Closeness(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]24.15 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_closseness, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","In Closeness(median)", "Out Closeness(median)", "Total Closeness(median)","In Closeness Normalized(median)", "Out Closeness Normalized(median)", "Total Closeness Normalized(median)", "Centralization Closeness(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]
#Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(6) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","In Closeness(M)", "In Closeness(median)", "Out Closeness(M)", "Out Closeness(median)", "Total Closeness(M)","Total Closeness(median)","In Closeness Normalized(M)", "In Closeness Normalized(median)", "Out Closeness Normalized(M)", "Out Closeness Normalized(median)", "Total Closeness Normalized(M)","Total Closeness Normalized(median)", "Centralization Closeness(M)","Centralization Closeness(median)")]24.16 Plotting final table with round for Closseness
datatable(total_table, filter = 'top')25 Betweenness - Number of shortest paths going through the actor σst(i)
High betweenness centrality - vertex lies on many shortest paths. Probability that a communication from s to t will go through i - considering σst(i).
Betweenness measures the number of shortest paths between nodes in the network that go through the node in question. Nodes with relatively high betweenness are likely to be key conduits of information flow across a network, and their removal may have a large impact on spreading phenomena.
25.1 Betweenness Centrality -(Vertex)
Betweenness centrality based on a broker position connecting others or Number of geodesics that pass through the node or the edge. A higher number means an more important node.
26 Adding weight equal one for all analysis
E(x2_without_CAPS)$equalone<-126.0.1 Saving objects
V(x2_without_CAPS)$x2_betweenness <- betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$equalone) %>% round(6)
x2_without_CAPS_betweenness <- betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$equalone) %>% round(6)
#Z Score
V(x2_without_CAPS)$x2_without_CAPS_betweenness_zscore <- (V(x2_without_CAPS)$x2_betweenness - mean(V(x2_without_CAPS)$x2_betweenness))/sd(V(x2_without_CAPS)$x2_betweenness)
#Normalized
V(x2_without_CAPS)$x2_without_CAPS_betweenness_norm <- (V(x2_without_CAPS)$x2_betweenness - min(V(x2_without_CAPS)$x2_betweenness))/max(V(x2_without_CAPS)$x2_betweenness)-min(V(x2_without_CAPS)$x2_betweenness)26.0.2 Betweenness Centrality - all
summary(x2_without_CAPS_betweenness)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 18.83 228.00 198.60 8716.00sd(x2_without_CAPS_betweenness)## [1] 756.039226.1 Betweenness Centrality Weighted - (Vertex)
V(x2_without_CAPS)$x2_betweenness_w <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$x2) %>% round(6)
x2_betweenness_w <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$x2) %>% round(6)26.1.1 Descriptive Betweenness Centrality Weighted - (Vertex) - all
summary(x2_betweenness_w)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 18.83 228.00 198.60 8716.00sd(x2_betweenness_w)## [1] 756.039226.2 Centralization Betweenness
V(x2_without_CAPS)$x2_centr_betweenness <- centralization.betweenness(x2_without_CAPS)$res
x2_centr_betweenness <- centralization.betweenness(x2_without_CAPS)26.2.1 Centralization
x2_centr_betweenness$centralization## [1] 0.250693926.2.2 Theoretical Max
x2_centr_betweenness$theoretical_max## [1] 629740027 Betweenness Vertex Centrality Dinamic Table
#Betweenness Vertex Centrality Measures Dinamic Table
#Getting Measures
x2_without_CAPS_betweenness <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$equalone) %>% round(6)
x2_betweenness_w <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$x2) %>% round(6)
x2_centr_betweenness <- centralization.betweenness(x2_without_CAPS)$res %>% round(6)
#Creating a dataframe of measures
x2_without_CAPS_df_betweenness <- data.frame(x2_without_CAPS_betweenness,
x2_betweenness_w,
x2_centr_betweenness) %>% round(6)
#Adding type
x2_without_CAPS_df_betweenness <-cbind(x2_without_CAPS_df_betweenness, V(x2_without_CAPS)$LABEL_COR)
#Adding names
names(x2_without_CAPS_df_betweenness) <- c("Betweenness", "Betweenness Weighted", "Centralization Betweenness","Type")
#Ordering Variables
x2_without_CAPS_df_betweenness<-x2_without_CAPS_df_betweenness[c("Type","Betweenness", "Betweenness Weighted", "Centralization Betweenness")]27.1 General tabel for Betweenness
datatable(x2_without_CAPS_df_betweenness, filter = 'top')aggdata_mean <-aggregate(x2_without_CAPS_df_betweenness, by=list(x2_without_CAPS_df_betweenness$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Betweenness(M)", "Betweenness Weighted(M)", "Centralization Betweenness(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]27.2 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_betweenness, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","Betweenness(median)", "Betweenness Weighted(median)", "Centralization Betweenness(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]27.3 Merging mean and median
total_table<- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(1) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","Betweenness(M)","Betweenness(median)","Betweenness Weighted(M)", "Betweenness Weighted(median)", "Centralization Betweenness(M)","Centralization Betweenness(median)")]27.4 Plotting final table with round
datatable(total_table, filter = 'top')28 Betweenness Vertex Centrality Dinamic Table (Natureza Governamental)
#Betweenness Vertex Centrality Measures Dinamic Table
#Getting Measures
x2_without_CAPS_betweenness <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$equalone) %>% round(6)
x2_betweenness_w <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$x2) %>% round(6)
x2_centr_betweenness <- centralization.betweenness(x2_without_CAPS)$res %>% round(6)
#Creating a dataframe of measures
x2_without_CAPS_df_betweenness <- data.frame(x2_without_CAPS_betweenness,
x2_betweenness_w,
x2_centr_betweenness) %>% round(6)
#Adding type
x2_without_CAPS_df_betweenness <-cbind(x2_without_CAPS_df_betweenness, V(x2_without_CAPS)$TIPO1)
#Adding names
names(x2_without_CAPS_df_betweenness) <- c("Betweenness", "Betweenness Weighted", "Centralization Betweenness","Type")
#Ordering Variables
x2_without_CAPS_df_betweenness<-x2_without_CAPS_df_betweenness[c("Type","Betweenness", "Betweenness Weighted", "Centralization Betweenness")]28.1 General tabel for Betweenness
datatable(x2_without_CAPS_df_betweenness, filter = 'top')aggdata_mean <-aggregate(x2_without_CAPS_df_betweenness, by=list(x2_without_CAPS_df_betweenness$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Betweenness(M)", "Betweenness Weighted(M)", "Centralization Betweenness(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]28.2 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_betweenness, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","Betweenness(median)", "Betweenness Weighted(median)", "Centralization Betweenness(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]28.3 Merging mean and median
total_table<- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(6) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","Betweenness(M)","Betweenness(median)","Betweenness Weighted(M)", "Betweenness Weighted(median)", "Centralization Betweenness(M)","Centralization Betweenness(median)")]28.4 Plotting final table with round
datatable(total_table, filter = 'top')29 Betweenness Vertex Centrality Dinamic Table (Setores)
#Betweenness Vertex Centrality Measures Dinamic Table
#Getting Measures
x2_without_CAPS_betweenness <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$equalone) %>% round(6)
x2_betweenness_w <- betweenness(x2_without_CAPS, weights=E(x2_without_CAPS)$x2) %>% round(1)
x2_centr_betweenness <- centralization.betweenness(x2_without_CAPS)$res %>% round(6)
#Creating a dataframe of measures
x2_without_CAPS_df_betweenness <- data.frame(x2_without_CAPS_betweenness,
x2_betweenness_w,
x2_centr_betweenness) %>% round(6)
#Adding type
x2_without_CAPS_df_betweenness <-cbind(x2_without_CAPS_df_betweenness, V(x2_without_CAPS)$TIPO2)
#Adding names
names(x2_without_CAPS_df_betweenness) <- c("Betweenness", "Betweenness Weighted", "Centralization Betweenness","Type")
#Ordering Variables
x2_without_CAPS_df_betweenness<-x2_without_CAPS_df_betweenness[c("Type","Betweenness", "Betweenness Weighted", "Centralization Betweenness")]29.1 General tabel for Betweenness
datatable(x2_without_CAPS_df_betweenness, filter = 'top')29.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_df_betweenness, by=list(x2_without_CAPS_df_betweenness$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Betweenness(M)", "Betweenness Weighted(M)", "Centralization Betweenness(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]29.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_df_betweenness, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","Betweenness(median)", "Betweenness Weighted(median)", "Centralization Betweenness(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]29.4 Merging mean and median
total_table<- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(6) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","Betweenness(M)","Betweenness(median)","Betweenness Weighted(M)", "Betweenness Weighted(median)", "Centralization Betweenness(M)","Centralization Betweenness(median)")]29.5 Plotting final table with round
datatable(total_table, filter = 'top')29.6 Plotting Betweenness Centrality - (Vertex)
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#Plotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$color[edge.start],
edge.arrow.size=(betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2)+1)/100000,
edge.width=E(x2_without_CAPS)$weight/10*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$color,
vertex.size=betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2 )/150,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=(betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2)+1)/10000,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$LABEL_COR
b<-V(x2_without_CAPS)$color
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Vertex Betweenness Sized - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf("Median Betweenness: %.2f\nSD Betweenness: %.2f",
median(betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2)),
sd(betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2))
)
)
29.7 Network Plotting Based On Centralization Betweenness
#Get Variable
V(x2_without_CAPS)$x2_centr_betweenness<-(centralization.betweenness(x2_without_CAPS)$res)/100
V(x2_without_CAPS)$x2_color_degree<-round(V(x2_without_CAPS)$x2_centr_betweenness,6)
#Creating brewer pallette
x2_vertex_color_degree<-
colorRampPalette(brewer.pal(length(unique(
V(x2_without_CAPS)$x2_color_degree)), "Spectral"))(
length(unique(V(x2_without_CAPS)$x2_color_degree)))
#Saving as Vertex properties
V(x2_without_CAPS)$x2_vertex_color_degree<-
x2_vertex_color_degree[as.numeric(
cut(V(x2_without_CAPS)$x2_color_degree,
breaks=length(unique(V(x2_without_CAPS)$x2_color_degree))))]
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS, es=E(x2_without_CAPS), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS))
maxC <- rep(Inf, vcount(x2_without_CAPS))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights = E(x2_without_CAPS)$weight)
#PLotting
plot(x2_without_CAPS,
layout=co,
edge.color=V(x2_without_CAPS)$x2_vertex_color_degree[edge.start],
edge.arrow.size=closeness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2, mode="out"),
edge.width=E(x2_without_CAPS)$weight/10*mean(E(x2_without_CAPS)$weight),
edge.curved = TRUE,
vertex.color=V(x2_without_CAPS)$x2_vertex_color_degree,
vertex.size=(centralization.betweenness(x2_without_CAPS)$res+1)/100,
vertex.frame.color="white",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS,"LABEL_COR"),
vertex.label.cex=(centralization.betweenness(x2_without_CAPS)$res + 1)/10000,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS)$x2_color_degree
b<-V(x2_without_CAPS)$x2_vertex_color_degree
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
e<-e[order(e$a,decreasing=T),]
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Centralization Betweenness - 1.2 - ALGUM RELACIONAMENTO (x2)", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf("Median Betweenness:%.0f\nSDBetweenness: %.0f",
median(betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2)),
sd(betweenness(x2_without_CAPS, weights = E(x2_without_CAPS)$x2))
)
)
30 Reciprocity Default
Reciprocity Default - Proportion of mutual connections - probability that hte opposite counterpart of a directed graph is also included
reciprocity(x2_without_CAPS, mode="default")## [1] 0.348473631 Reciprocity Ratio
Reciprocity Ratio - Probability of mutual connections between a vertex pair - if we know - probability that hte opposite counterpart of a directed graph is also included in the
reciprocity(x2_without_CAPS, mode="ratio")## [1] 0.211000932 Dyad Census
A dyad consists of an unordered pair of actors and links that exist between two actors of the pair classified by mutal non-mutual and no connection in a directed graphs
Dyads are 2-subgraphs where a subgraph is a subset of actors taken from the complete set of network actors and all links between them. See more here http://file.scirp.org/pdf/SN_2013012915270187.pdf
32.1 Dyad Census
Number of pairs with mutual connections “mut” and number of pairs with non-mutual connections “asym”
dyad.census_x2_without_CAPS<-dyad.census(x2_without_CAPS)32.2 Mutual connections.
dyad.census_x2_without_CAPS_mut<-dyad.census_x2_without_CAPS$mut
dyad.census_x2_without_CAPS_mut## [1] 23632.3 Non-mutual connections.
dyad.census_x2_without_CAPS_asym<-dyad.census_x2_without_CAPS$asym
dyad.census_x2_without_CAPS_asym## [1] 87532.4 No connection between them.
dyad.census_x2_without_CAPS_null<-dyad.census_x2_without_CAPS$null
dyad.census_x2_without_CAPS_null## [1] 1609433 Triad Census - Check this out in order to understand triad lables
The studies about transitivity in social networks led Holland and Leinhardt (1975) to propose that the local structure in social networks can be expressed by the triad census or triad count, the numbers of triads of any kinds.
You can see more here: http://www.stats.ox.ac.uk/~snijders/Trans_Triads_ha.pdf
#Triad Census
tc_x2_without_CAPS <- triad.census(x2_without_CAPS)
#Triad Census Label
census_labels = c('T.003',
'T.012',
'T.102',
'T.021D',
'T.021U',
'T.021C',
'T.111D',
'T.111U',
'T.030T',
'T.030C',
'T.201',
'T.120D',
'T.120U',
'T.120C',
'T.210',
'T.300')
ordering = c('1',
'2',
'3',
'4',
'5',
'6',
'7',
'8',
'13',
'10',
'9',
'14',
'15',
'11',
'12',
'16')
#Saving in a dataframe for further studies
triad_df_x2_without_CAPS <- data.frame(census_labels,tc_x2_without_CAPS)
write.csv(triad_df_x2_without_CAPS, "~/SNArRDJF/Banco Redes R/x2_without_CAPS_complet_triads.csv")33.1 Triad Census Types
The following labels gives the 16 different triads for directed graphs. The coding refers to the numbers of mutual, asymmetric, and null dyads, with a further identifying letter: Up, Down, Cyclical, Transitive.
E.g., 1-2-0-D has 1 mutual, 2 asymmetric, 0 null dyads, and the Down orientation.
33.1.1 Describing triads
triad_df_x2_without_CAPS## census_labels tc_x2_without_CAPS
## 1 T.003 880032
## 2 T.012 118577
## 3 T.102 30348
## 4 T.021D 7099
## 5 T.021U 2530
## 6 T.021C 4856
## 7 T.111D 2773
## 8 T.111U 5099
## 9 T.030T 950
## 10 T.030C 71
## 11 T.201 1361
## 12 T.120D 289
## 13 T.120U 465
## 14 T.120C 316
## 15 T.210 378
## 16 T.300 9633.1.2 Triads Tables Recoding
#Recoding different types of triads
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.003"]<-"Vacuously Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.012"]<-"Vacuously Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.102"]<-"Vacuously Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.021D"]<-"Vacuously Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.021U"]<-"Vacuously Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.021C"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.111D"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.111U"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.030T"]<-"Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.030C"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.201"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.120D"]<-"Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.120U"]<-"Transitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.120C"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.210"]<-"Intransitive"
triad_df_x2_without_CAPS$type[triad_df_x2_without_CAPS$census_labels=="T.300"]<-"Transitive"Graphical Ilustration
33.1.3 Triads Tables
datatable(triad_df_x2_without_CAPS)34 Transitivity - clustering coefficient
34.1 Transitivity Global
Socialnetwork is treated as an undirected network global - ratio of triangles (direction disregarded) to connected triples.
transitivity(x2_without_CAPS, type="global")## [1] 0.244962335 Transitivity Local
Ratio of triangles to connected triples each vertex is part of.
V(x2_without_CAPS)$x2_transitivity_local<-transitivity(x2_without_CAPS, type="local")
x2_without_CAPS_transitivity_local<-transitivity(x2_without_CAPS, type="local") #local - ratio of triangles to connected triples each vertex is part of.36 Descriptive Statistics for Local Transitivity by Vertex
summary(x2_without_CAPS_transitivity_local[which(x2_without_CAPS_transitivity_local != Inf)])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.2022 0.3198 0.3567 0.4738 1.0000sd(x2_without_CAPS_transitivity_local[which(x2_without_CAPS_transitivity_local != Inf)])## [1] 0.22274237 Barrat’s Weighted Transitivity by Edges (Barrat’s)
V(x2_without_CAPS)$x2_transitivity_barrat<-transitivity(x2_without_CAPS, weights=E(x2_without_CAPS)$weight, type="barrat")
x2_without_CAPS_transitivity_barrat<-transitivity(x2_without_CAPS, weights=E(x2_without_CAPS)$weight, type="barrat")38 Descriptive Statistics for Barrat Weighted Transitivity by Vertex
summary(x2_without_CAPS_transitivity_barrat[which(x2_without_CAPS_transitivity_barrat != Inf)])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.3560 0.5000 0.5646 0.7130 1.6670sd(x2_without_CAPS_transitivity_barrat[which(x2_without_CAPS_transitivity_barrat != Inf)])## [1] 0.322445739 Transitivity Measures Dinamic Table
#Getting Measures
x2_without_CAPS_transitivity_local<-transitivity(x2_without_CAPS, type="local") %>% round(3)
x2_without_CAPS_transitivity_barrat<-transitivity(x2_without_CAPS, weights=E(x2_without_CAPS)$weight, type="barrat") %>% round(3)
#Creating a datagrame of measures
x2_without_CAPS_transitivity_df <- data.frame(x2_without_CAPS_transitivity_local,x2_without_CAPS_transitivity_barrat) %>% round(3)40 Transitivity Measures Dinamic Table
x2_without_CAPS_transitivity_df <-cbind(x2_without_CAPS_transitivity_df, V(x2_without_CAPS)$LABEL_COR)
#Adding names
names(x2_without_CAPS_transitivity_df) <- c("Local", "Barrat's Weighted","Type")
#Ordering Variables
x2_without_CAPS_transitivity_df<-x2_without_CAPS_transitivity_df[c("Type", "Local", "Barrat's Weighted")]40.1 General tabel - DT
datatable(x2_without_CAPS_transitivity_df, filter = 'top')40.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_transitivity_df, by=list(x2_without_CAPS_transitivity_df$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Local(M)", "Barrat's Weighted(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]40.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_transitivity_df, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","Local(median)", "Barrat's Weighted(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]40.4 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(3) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","Local(M)","Local(median)", "Barrat's Weighted(M)","Barrat's Weighted(median)")]40.5 Final table with round - Transitivity
datatable(total_table, filter = 'top')41 Transitivity Measures Dinamic Table
#Getting Measures
x2_without_CAPS_transitivity_local<-transitivity(x2_without_CAPS, type="local") %>% round(3)
x2_without_CAPS_transitivity_barrat<-transitivity(x2_without_CAPS, weights=E(x2_without_CAPS)$weight, type="barrat") %>% round(3)
#Creating a datagrame of measures
x2_without_CAPS_transitivity_df <- data.frame(x2_without_CAPS_transitivity_local,x2_without_CAPS_transitivity_barrat) %>% round(3)42 Transitivity Measures Dinamic Table
x2_without_CAPS_transitivity_df <-cbind(x2_without_CAPS_transitivity_df, V(x2_without_CAPS)$TIPO1)
#Adding names
names(x2_without_CAPS_transitivity_df) <- c("Local", "Barrat's Weighted","Type")
#Ordering Variables
x2_without_CAPS_transitivity_df<-x2_without_CAPS_transitivity_df[c("Type", "Local", "Barrat's Weighted")]42.1 General tabel - DT
datatable(x2_without_CAPS_transitivity_df, filter = 'top')42.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_transitivity_df, by=list(x2_without_CAPS_transitivity_df$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Local(M)", "Barrat's Weighted(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]42.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_transitivity_df, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","Local(median)", "Barrat's Weighted(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]42.4 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(3) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","Local(M)","Local(median)", "Barrat's Weighted(M)","Barrat's Weighted(median)")]42.5 Final table with round - Transitivity
datatable(total_table, filter = 'top')43 Transitivity Measures Dinamic Table
#Getting Measures
x2_without_CAPS_transitivity_local<-transitivity(x2_without_CAPS, type="local") %>% round(3)
x2_without_CAPS_transitivity_barrat<-transitivity(x2_without_CAPS, weights=E(x2_without_CAPS)$weight, type="barrat") %>% round(3)
#Creating a datagrame of measures
x2_without_CAPS_transitivity_df <- data.frame(x2_without_CAPS_transitivity_local,x2_without_CAPS_transitivity_barrat) %>% round(3)44 Transitivity Measures Dinamic Table
x2_without_CAPS_transitivity_df <-cbind(x2_without_CAPS_transitivity_df, V(x2_without_CAPS)$TIPO2)
#Adding names
names(x2_without_CAPS_transitivity_df) <- c("Local", "Barrat's Weighted","Type")
#Ordering Variables
x2_without_CAPS_transitivity_df<-x2_without_CAPS_transitivity_df[c("Type", "Local", "Barrat's Weighted")]44.1 General tabel - DT
datatable(x2_without_CAPS_transitivity_df, filter = 'top')44.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_transitivity_df, by=list(x2_without_CAPS_transitivity_df$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Local(M)", "Barrat's Weighted(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]44.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_transitivity_df, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group","Local(median)", "Barrat's Weighted(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]44.4 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(3) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[c("Group","Local(M)","Local(median)", "Barrat's Weighted(M)","Barrat's Weighted(median)")]44.5 Final table with round - Transitivity
datatable(total_table, filter = 'top')45 Distances and paths
Defined as the shortest distance between each pair of nodes in the network (in both directions for directed graphs).
45.1 Average path length between any two given nodes
Calculates the average path length in a graph, by calculating the shortest paths between all pairs of vertices (both ways for directed graphs).
This function does not consider edge weights currently and uses a breadth-first search.
mean_distance(x2_without_CAPS, directed=T, unconnected = T)## [1] 2.72859645.2 Shortest Paths
#Shortest Paths
x2_without_CAPS_sp_in <- shortest.paths(x2_without_CAPS, mode='in', weights=E(x2_without_CAPS)$x2) #in
x2_without_CAPS_sp_out <- shortest.paths(x2_without_CAPS, mode='out', weights=E(x2_without_CAPS)$x2) # out
x2_without_CAPS_sp_all <- shortest.paths(x2_without_CAPS, mode='all', weights=E(x2_without_CAPS)$x2) # all45.3 Descriptive Shortest Paths - IN
summary(x2_without_CAPS_sp_in[which(x2_without_CAPS_sp_in != Inf)])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 2.000 3.000 2.708 3.000 6.000sd(x2_without_CAPS_sp_in[which(x2_without_CAPS_sp_in != Inf)])## [1] 0.947038745.4 Descriptive Shortest Paths - OUT
summary(x2_without_CAPS_sp_out[which(x2_without_CAPS_sp_out != Inf)])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 2.000 3.000 2.708 3.000 6.000sd(x2_without_CAPS_sp_out[which(x2_without_CAPS_sp_out != Inf)])## [1] 0.947038745.5 Descriptive Shortest Paths - ALL
summary(x2_without_CAPS_sp_all[which(x2_without_CAPS_sp_all != Inf)])## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 2.000 2.000 2.355 3.000 5.000sd(x2_without_CAPS_sp_all[which(x2_without_CAPS_sp_all != Inf)])## [1] 0.716087346 Length of all shortest paths in the graph:
#All shortest paths
distances_dist_all_x2_without_CAPS<-distances(x2_without_CAPS, mode="all", weights=E(x2_without_CAPS)$x2)
#distances_sp_all_x2_without_CAPS
distances_dist_all_x2_without_CAPS[distances_dist_all_x2_without_CAPS=="Inf"]<-NA
#Mean Reachbility by Vertex
distances_sp_all_x2_without_CAPS_vec <- vector()
for (i in 1:vcount(x2_without_CAPS)) {
distances_sp_all_x2_without_CAPS_vec[i] <-
mean(distances_dist_all_x2_without_CAPS[i,],na.rm=T)
}
#Adding to igraph object
V(x2_without_CAPS)$x2_sp_all<-distances_sp_all_x2_without_CAPS_vec47 In shortest paths
distances_dist_in_x2_without_CAPS<-distances(x2_without_CAPS, mode="in",weights=E(x2_without_CAPS)$x2)
#distances_sp_in_x2_without_CAPS
distances_dist_in_x2_without_CAPS[distances_dist_in_x2_without_CAPS=="Inf"]<-NA
#Mean Reachbility by Vertex
distances_sp_in_x2_without_CAPS_vec <- vector()
for (i in 1:vcount(x2_without_CAPS)) {
distances_sp_in_x2_without_CAPS_vec[i] <- mean(distances_dist_in_x2_without_CAPS[i,], na.rm=T)
}
#Adding to igraph object
V(x2_without_CAPS)$x2_sp_in<-distances_sp_in_x2_without_CAPS_vec48 Out shortest paths
distances_dist_out_x2_without_CAPS<-distances(x2_without_CAPS, mode="out", weights=E(x2_without_CAPS)$x2)
distances_dist_out_x2_without_CAPS[distances_dist_out_x2_without_CAPS=="Inf"]<-NA
#Mean Reachbility by Vertex
distances_sp_out_x2_without_CAPS_vec <- vector()
for (i in 1:vcount(x2_without_CAPS)) {
distances_sp_out_x2_without_CAPS_vec[i] <-
mean(distances_dist_out_x2_without_CAPS[i,], na.rm = T)
}
#Adding to igraph object
V(x2_without_CAPS)$x2_sp_out<-distances_sp_out_x2_without_CAPS_vec49 Reachbility Measures Dinamic Table
#Creating a datagrame of measures
x2_without_CAPS_shortpath_df <- data.frame(distances_sp_in_x2_without_CAPS_vec, distances_sp_out_x2_without_CAPS_vec, distances_sp_all_x2_without_CAPS_vec) %>% round(3)
#Adding type
x2_without_CAPS_shortpath_df <-cbind(x2_without_CAPS_shortpath_df, V(x2_without_CAPS)$LABEL_COR)
#Adding names
names(x2_without_CAPS_shortpath_df) <- c("Short Path IN", "Short Path OUT","Short Path ALL","Type")
#Ordering Variables
x2_without_CAPS_shortpath_df<-x2_without_CAPS_shortpath_df[c("Type", "Short Path IN", "Short Path OUT","Short Path ALL")]49.1 General tabel - DT
datatable(x2_without_CAPS_shortpath_df, filter = 'top')49.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_shortpath_df, by=list(x2_without_CAPS_shortpath_df$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Short Path IN(M)", "Short Path OUT(M)","Short Path ALL(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]49.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_shortpath_df, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group", "Short Path IN(median)", "Short Path OUT(median)","Short Path ALL(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]49.4 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(3) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[,c("Group","Short Path IN(M)","Short Path IN(median)","Short Path OUT(M)","Short Path OUT(median)","Short Path ALL(M)","Short Path ALL(median)")]49.5 Final table with round - Short Path
datatable(total_table, filter = 'top')50 Reachbility Measures Dinamic Table
#Creating a datagrame of measures
x2_without_CAPS_shortpath_df <- data.frame(distances_sp_in_x2_without_CAPS_vec, distances_sp_out_x2_without_CAPS_vec, distances_sp_all_x2_without_CAPS_vec) %>% round(3)
#Adding type
x2_without_CAPS_shortpath_df <-cbind(x2_without_CAPS_shortpath_df, V(x2_without_CAPS)$TIPO1)
#Adding names
names(x2_without_CAPS_shortpath_df) <- c("Short Path IN", "Short Path OUT","Short Path ALL","Type")
#Ordering Variables
x2_without_CAPS_shortpath_df<-x2_without_CAPS_shortpath_df[c("Type", "Short Path IN", "Short Path OUT","Short Path ALL")]50.1 General tabel - DT
datatable(x2_without_CAPS_shortpath_df, filter = 'top')50.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_shortpath_df, by=list(x2_without_CAPS_shortpath_df$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Short Path IN(M)", "Short Path OUT(M)","Short Path ALL(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]50.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_shortpath_df, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group", "Short Path IN(median)", "Short Path OUT(median)","Short Path ALL(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]50.4 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(3) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[,c("Group","Short Path IN(M)","Short Path IN(median)","Short Path OUT(M)","Short Path OUT(median)","Short Path ALL(M)","Short Path ALL(median)")]50.5 Final table with round - Short Path
datatable(total_table, filter = 'top')51 Reachbility Measures Dinamic Table
#Creating a datagrame of measures
x2_without_CAPS_shortpath_df <- data.frame(distances_sp_in_x2_without_CAPS_vec, distances_sp_out_x2_without_CAPS_vec, distances_sp_all_x2_without_CAPS_vec) %>% round(3)
#Adding type
x2_without_CAPS_shortpath_df <-cbind(x2_without_CAPS_shortpath_df, V(x2_without_CAPS)$TIPO2)
#Adding names
names(x2_without_CAPS_shortpath_df) <- c("Short Path IN", "Short Path OUT","Short Path ALL","Type")
#Ordering Variables
x2_without_CAPS_shortpath_df<-x2_without_CAPS_shortpath_df[c("Type", "Short Path IN", "Short Path OUT","Short Path ALL")]51.1 General tabel - DT
datatable(x2_without_CAPS_shortpath_df, filter = 'top')51.2 Aggregating data from previous table - mean
aggdata_mean <-aggregate(x2_without_CAPS_shortpath_df, by=list(x2_without_CAPS_shortpath_df$Type), FUN=mean, na.rm=TRUE)
names(aggdata_mean) <- c("Group","Type","Short Path IN(M)", "Short Path OUT(M)","Short Path ALL(M)")
#Removing Type variable
aggdata_mean<-aggdata_mean[,-c(2)]51.3 Aggregating data from previous table - median
aggdata_median <-aggregate(. ~ Type, x2_without_CAPS_shortpath_df, function(x) c(median=median(x)))
names(aggdata_median) <- c("Group", "Short Path IN(median)", "Short Path OUT(median)","Short Path ALL(median)")
#Removing Type variable
#aggdata_median<-aggdata_median[,-c(2)]51.4 Merging mean and median
total_table <- merge(aggdata_mean,aggdata_median,by="Group")
#Rounding
Group<-total_table[,c(1)] #Keeping group
total_table<-total_table[,-c(1)] %>% round(3) #Rouding
total_table<-cbind(Group,total_table) #Binding toghter
#Organizing Variabels
total_table<-total_table[,c("Group","Short Path IN(M)","Short Path IN(median)","Short Path OUT(M)","Short Path OUT(median)","Short Path ALL(M)","Short Path ALL(median)")]51.5 Final table with round - Short Path
datatable(total_table, filter = 'top')51.6 Histogram from shortest path length between each pair of vertices.
sp<-distance_table(x2_without_CAPS, directed = TRUE)
short_paths<-c(sp$unconnected, sp$res)
labels<-c("unconnected", "one", "two","three", "four", "five", "six")
sphist<-as.data.frame(cbind(labels, short_paths))
names(sphist)<-c("Short Paths Length - Vertex Pairs","Count")
datatable(sphist)51.7 Simplify Graph - removing loops and duble edges
#x2_without_CAPS_u<-simplify(x2_without_CAPS) #Simplify
x2_without_CAPS_u<-as.undirected(x2_without_CAPS, mode="collapse",edge.attr.comb=list(weight="mean","ignore"))52 Find cliques (complete subgraphs of an undirected graph)
Graph clique is a subset of vertices of a graph such that every two vertices in the clique are adjacent. - To check*
52.1 Number of cliques - subgraphs
cliques_x2_without_CAPS_u<-cliques(x2_without_CAPS_u) # list of cliques
length(cliques_x2_without_CAPS_u)## [1] 1951852.2 Number of cliques by cliques size
cliques_x2_without_CAPS_u_size<-sapply(cliques(x2_without_CAPS_u), length)
cliques_x2_without_CAPS_u_size_t<-table(cliques_x2_without_CAPS_u_size)
cliques_x2_without_CAPS_u_size_t## cliques_x2_without_CAPS_u_size
## 1 2 3 4 5 6 7 8 9 10
## 186 1109 2565 4107 4748 3849 2084 715 142 1352.3 Cliques Bar Plot Sizes Frequency
barplot(cliques_x2_without_CAPS_u_size_t)
title(main = "Cliques Sizes Frequency - Bar Plot 1.2 - ALGUM RELACIONAMENTO (x2)", font.main = 4)
52.4 Size of largest clique
A maximum clique is a clique that cannot be extended by including one more adjacent vertex (not included in larger one).
clique_num(x2_without_CAPS_u)## [1] 1052.5 Number of maximal cliques
count_max_cliques(x2_without_CAPS_u)## [1] 64252.6 Finding of largest cliques
largest_cliques<-largest_cliques(x2_without_CAPS_u) # cliques with max number of nodes
length(largest_cliques)## [1] 1352.7 Plotting the largest cliques - important to consider connectivite
#Coloring largest clique as gold and others one as gray
vcol <- rep("grey80", vcount(x2_without_CAPS_u))
vcol[unlist(largest_cliques(x2_without_CAPS_u))] <- "gold"
#Saving gray and gold as igraph attribute
V(x2_without_CAPS_u)$vcol<-vcol
#Saving labels to display as legend
V(x2_without_CAPS_u)$vcollabel[V(x2_without_CAPS_u)$vcol=="gold"]<-"Largets Clique"
V(x2_without_CAPS_u)$vcollabel [V(x2_without_CAPS_u)$vcol=="grey80"]<-"Others"52.8 Plotting Clique Size
set.seed(123)
#Plotting based only on degree measures
edge.start <- ends(x2_without_CAPS_u, es=E(x2_without_CAPS_u), names=F)[,1]
# Fixing ego
minC <- rep(-Inf, vcount(x2_without_CAPS_u))
maxC <- rep(Inf, vcount(x2_without_CAPS_u))
minC[1] <- maxC[1] <- 0
co <- layout_with_fr(x2_without_CAPS_u, niter=10^4, minx=minC, maxx=maxC,miny=minC, maxy=maxC, weights=E(x2_without_CAPS_u)$x2_without_CAPS)
#Plotting
plot(x2_without_CAPS_u,
layout=co,
edge.color=V(x2_without_CAPS_u)$vcol[edge.start],
#edge.arrow.size=E(x2_without_CAPS_u)$x2_without_CAPS/2000*mean(E(x2_without_CAPS_u)$x2_without_CAPS),
#edge.width=E(x2_without_CAPS_u)$x2_without_CAPS/20*mean(E(x2_without_CAPS_u)$x2_without_CAPS),
edge.curved = TRUE,
vertex.color=vcol,
vertex.size=log(degree(x2_without_CAPS_u)+2)*10,
vertex.frame.color="black",
vertex.label.color="black",
vertex.label=get.vertex.attribute(x2_without_CAPS_u,"LABEL_COR"),
vertex.label.cex=log(degree(x2_without_CAPS_u)+2)/10,
vertex.label.dist=0,
rescale=F,
xlim=range(co[,1]),
ylim=range(co[,2])
)
axis(1)
axis(2)
#Solving Problems with legend rendering
a<-V(x2_without_CAPS_u)$vcollabel
b<-V(x2_without_CAPS_u)$vcol
c<-table(a,b)
d<-as.data.frame(c)
e<-subset(d, d$Freq>0)
f<-t(e$a)
g<-t(e$b)
#Adding Legend
legend(x=range(co[,1])[2],
y=range(co[,2])[2],
legend=as.character(f),
pch=21,
col = "#777777",
pt.bg=as.character(g),
pt.cex=2,
bty="n",
ncol=1,
lty=1,
cex = .3)
#Adding Title
title("Network Vertex Degree Sized - classfied by largest clique vs. others", sub = "Source: from authors ")
text(
x=range(co[,1])[1],
y=range(co[,2])[1],
labels = sprintf("Size of largest clique: %.1f\nNumber of maximal cliques: %.1f",
clique_num(x2_without_CAPS_u),
count_max_cliques(x2_without_CAPS_u)
)
)
# Re-generate dataframes for both nodes and edges, now containing
# calculated network attributes
x2_without_CAPS_node_list <- get.data.frame(x2_without_CAPS, what = "vertices")
#Write Node List
write.csv(x2_without_CAPS_node_list, "~/SNArRDJF/Tese_Pedro/SemCAPS/Banco/x2_without_CAPS_node_list_df.csv")
# Determine a community for each edge. If two nodes belong to the
# same community, label the edge with that community. If not,
# the edge community value is 'NA'
x2_without_CAPS_edge_list <- get.data.frame(x2_without_CAPS, what = "edges")
#Write Node List
write.csv(x2_without_CAPS_edge_list, "~/SNArRDJF/Tese_Pedro/SemCAPS/Banco/x2_without_CAPS_edge_list.csv")
#Write Node List
write.csv(x2_without_CAPS_edge_list, "~/SNArRDJF/Tese_Pedro/SemCAPS/Banco/x2_without_CAPS_edge_list.csv")53 Saving objects with new variables and changes
save.image("~/SNArRDJF/Robject/x2_without_CAPS_dataframe.RData")